Airfoil shape for turbine nozzles

ABSTRACT

A turbine nozzle having an airfoil that includes a pressure side portion of a nominal airfoil profile substantially in accordance with Cartesian coordinate values of X, Y, and Z of a pressure side as set forth in Table I. The Cartesian coordinate values of X, Y, and Z are non-dimensional values from 0% to 100% convertible to dimensional distances by multiplying the Cartesian coordinate values of X, Y and Z by a height of the airfoil defined along the Z axis. The X and Y values of the pressure side are coordinate values that, when connected by smooth continuing arcs, define pressure side sections of the pressure side portion of the nominal airfoil profile at each Z coordinate value. The pressure side sections may be joined smoothly with one another to form the pressure side portion.

BACKGROUND OF THE INVENTION

The subject matter disclosed herein relates to turbine engine airfoils and, more specifically, to airfoils of stator blades or nozzles.

Some aircraft and/or power plant systems, for example certain jet aircraft, gas turbines, and combined cycle power plant systems, employ turbines (also referred to as turbomachines) in their design and operation. Some of these turbines employ airfoils (e.g., turbine stator blades, nozzles, etc.) which during operation are exposed to fluid flows. These airfoils are configured to aerodynamically interact with the fluid flows and generate energy (e.g., creating thrust, turning kinetic energy to mechanical energy, thermal energy to mechanical energy, etc.) from these fluid flows as part of power generation. As a result of this interaction and conversion, the aerodynamic characteristics and losses of these airfoils have an impact on system and turbine operation, performance, thrust, efficiency, and power.

BRIEF DESCRIPTION OF THE INVENTION

Aspects and advantages are set forth below in the following description, or may be obvious from the description, or may be learned through practice.

According to an exemplary embodiment, the present disclosure includes a turbine nozzle having an airfoil that includes a pressure side portion of a nominal airfoil profile substantially in accordance with Cartesian coordinate values of X, Y, and Z of a pressure side as set forth in Table I. The Cartesian coordinate values of X, Y, and Z are non-dimensional values from 0% to 100% convertible to dimensional distances by multiplying the Cartesian coordinate values of X, Y and Z by a height of the airfoil defined along the Z axis. The X and Y values of the pressure side are coordinate values that, when connected by smooth continuing arcs, define pressure side sections of the pressure side portion of the nominal airfoil profile at each Z coordinate value. The pressure side sections may be joined smoothly with one another to form the pressure side portion.

According to another exemplary embodiment, the present disclosure includes a turbine nozzle having an airfoil that includes a suction side portion of a nominal airfoil profile substantially in accordance with Cartesian coordinate values of X, Y, and Z of a suction side as set forth in Table I. The Cartesian coordinate values of X, Y, and Z are non-dimensional values from 0% to 100% convertible to dimensional distances by multiplying the Cartesian coordinate values of X, Y and Z by a height of the airfoil defined along the Z axis. The X and Y values of the suction side are coordinate values that, when connected by smooth continuing arcs, define suction side sections of the suction side portion of the nominal airfoil profile at each Z coordinate value. The suction side sections may be joined smoothly with one another to form the suction side portion.

According to another exemplary embodiment, the present disclosure includes a turbine engine that has an airfoil that includes: a pressure side portion of a nominal airfoil profile substantially in accordance with Cartesian coordinate values of X, Y, and Z of a pressure side as set forth in Table I; and a suction side portion of the nominal airfoil profile substantially in accordance with Cartesian coordinate values of X, Y, and Z of the suction side as set forth in Table I. The Cartesian coordinate values of X, Y, and Z are non-dimensional values from 0% to 100% convertible to dimensional distances by multiplying the Cartesian coordinate values of X, Y and Z by a height of the airfoil defined along the Z axis. The X and Y values of the pressure side are coordinate values that, when connected by smooth continuing arcs, define pressure side sections of the pressure side portion of the nominal airfoil profile at each Z coordinate value. The pressure side sections may be joined smoothly with one another to form the pressure side portion. The X and Y values of the suction side are coordinate values that, when connected by smooth continuing arcs, define suction side sections of the suction side portion of the nominal airfoil profile at each Z coordinate value. The suction side sections may be joined smoothly with one another to form the suction side portion.

Those of ordinary skill in the art will better appreciate the features and aspects of such embodiments, and others, upon review of the specification.

BRIEF DESCRIPTION OF THE DRAWINGS

A full and enabling disclosure of various embodiments, including the best mode thereof to one skilled in the art, is set forth more particularly in the remainder of the specification, including reference to the accompanying figures, in which:

FIG. 1 is a schematic representation of an exemplary turbine having multiple stages with each stage including alternating rows of turbine rotor blades and turbine nozzles according to at least one embodiment of the present disclosure;

FIG. 2 is a perspective view of an exemplary turbine nozzle according to at least one embodiment of the present disclosure; and

FIG. 3 provides a cross-sectional view of an airfoil portion of the turbine nozzle of FIG. 2.

DETAILED DESCRIPTION OF THE INVENTION

One or more specific embodiments of the present subject matter will be described below. In an effort to provide a concise description of these embodiments, all features of an actual implementation may not be described in the specification. It should be appreciated that in the development of any such actual implementation, as in any engineering or design project, numerous implementation-specific decisions must be made to achieve the developers' specific goals, such as compliance with system-related and business-related constraints, which may vary from one implementation to another. Moreover, it should be appreciated that such a development effort might be complex and time consuming, but would nevertheless be a routine undertaking of design, fabrication, and manufacture for those of ordinary skill having the benefit of this disclosure.

When introducing elements of various embodiments of the present subject matter, the articles “a,” “an,” “the,” and “said” are intended to mean that there are one or more of the elements. The terms “comprising,” “including,” and “having” are intended to be inclusive and mean that there may be additional elements other than the listed elements.

Referring now to the drawings, particularly to FIG. 1, there is illustrated an exemplary turbine 10 of a combustion or gas turbine 12 including a plurality of turbine stages arranged in serial flow order. Each stage of the turbine includes a row of turbine stator blades, vanes, or nozzles disposed axially adjacent to a corresponding row of turbine rotor blades. While four stages are illustrated in FIG. 1, the exact number of stages of the turbine 10 is a choice of engineering design, and may be more or less than the four stages shown. The four stages are merely exemplary of one turbine design, and are not intended to limit the presently claimed turbine rotor blade in any manner.

As depicted in FIG. 1, the first stage includes a plurality of turbine nozzles 100 and a plurality of turbine rotor blades 150. The turbine nozzles 100 are annularly arranged about an axis of a turbine rotor 14, while the turbine rotor blades 150 are annularly arranged about and coupled to the turbine rotor 14. A second stage of the turbine 12 includes a plurality of turbine nozzles 200 annularly arranged about the axis of the turbine rotor 14 and a plurality of turbine rotor blades 250 annularly arranged about and coupled to the turbine rotor 14. A third stage of the turbine 12 includes a plurality of turbine nozzles 300 annularly arranged about the axis of the turbine rotor 14 and a plurality of turbine rotor blades 350 annularly arranged about and coupled to the turbine rotor 14. In particular embodiments, the turbine 12 may further include a fourth stage, which also includes plurality of turbine nozzles 400 annularly arranged about the axis of the turbine rotor 14 and a plurality of turbine rotor blades 450 annularly arranged about and coupled to the turbine rotor 14. As will be appreciated, the turbine nozzles 100, 200, 300, 400 may be coupled to the casing of the turbine 12 and remain stationary during operation.

It will be appreciated that the turbine nozzles 100, 200, 300 and 400 and turbine rotor blades 150, 250, 350 and 450 are disposed or at least partially disposed within a working fluid flowpath or hot gas path 18 of the turbine 12. The various stages of the turbine 10 at least partially define the hot gas path 18 through which combustion gases, as indicated by arrows 20, flow during operation of the gas turbine 12.

FIG. 2 provides a perspective view of an exemplary turbine nozzle 50 as may be incorporated in one of the stages of the turbine 12. FIG. 3 provides a cross-sectional top view of an airfoil 52 of the turbine nozzle 50 shown in FIG. 2. In a preferred embodiment of the present disclosure, the turbine nozzle 50 (as described by the points included within Table I below) is a turbine nozzle 200 of the plurality of the turbine nozzles 200 used in the second stage of the turbine 12, as shown in FIG. 1. As illustrated in FIGS. 2 and 3 collectively, the turbine nozzle 50 airfoil 52 includes a pressure side 54 and an opposing suction side 56. The pressure side 54 and the suction side 56 meet or intersect at a leading edge 58 and at a trailing edge 60 of the airfoil 52. A chord line 62 extends between the leading edge 58 and the trailing edge 60 such that pressure and suction sides 54, 56 can be said to extend in chord or chordwise between the leading edge 58 and the trailing edge 60.

As shown in FIG. 2, the airfoil 52 further includes a first end or root 64, which intersects with and extends radially outwardly from an inner band 66 of the turbine nozzle 50. The airfoil 52 terminates radially at a second end or tip 68 of the airfoil 52. The second end 68 intersects with and extends radially inwardly from an outer band 70 of the turbine nozzle 50. The pressure and suction sides 54, 56 can be said to extend in span or a span-wise direction 72 (along the height of the airfoil 52) between the root 64 and/or the inner band 66 and the second end 68 or the outer band 70. In other words, each turbine nozzle 50 includes an airfoil 52 having opposing pressure and suction sides 54, 56 that extend in chord or chordwise 62 between opposing leading and trailing edges 58, 60 and that extend in span or span-wise 72 between the root 64 and the second end 68 of the airfoil 52.

In particular configurations, the airfoil 52 may include a fillet 74 formed between the inner band 66 and the airfoil 52 proximate to the root 64. The fillet 74 can include a weld or braze fillet, which can be formed via conventional MIG welding, TIG welding, brazing, etc., and the fillet 74 can have a profile that reduces fluid dynamic losses. In particular embodiments, the inner band 66, airfoil 52 and the fillet 74 can be formed as a single component, such as by casting and/or machining and/or 3D printing and/or any other suitable technique now known or later developed and/or discovered.

The airfoil 52 of the turbine nozzle 50 has a profile at any cross-section taken between the root 64 and the second end 68. In accordance with the present disclosure, the X, Y, and Z values of the profile are given in Table I as percentage values of the airfoil span or height. As one example, the height of the airfoil 52 of the turbine nozzle 50 may be from about 2 inches to about 50 inches. As another example, the height of the airfoil 52 of the turbine nozzle 50 may be from about 3 inches to about 10 inches. However, it is to be understood that heights below or above this range may also be employed as desired in the specific application.

A hot gas path of a gas turbine requires airfoils that meet system requirements of aerodynamic and mechanical blade loading and efficiency. To define the airfoil shape of each turbine nozzle airfoil, there is a unique set or locus of points in space that meet the stage requirements and that can be manufactured. This unique locus of points meets the requirements for stage efficiency and are arrived at by iteration between aerodynamic and mechanical loadings enabling the turbine to run in an efficient, safe and smooth manner. These points are unique and specific to the system.

The locus of points that defines the airfoil profile of a turbine nozzle includes a set of points with X, Y and Z dimensions relative to a reference origin coordinate system, as provided in Table I and shown in FIG. 2, respectively. The Cartesian coordinate system of X, Y and Z values given in Table I below defines the profile of the airfoil of a turbine nozzle at various locations along its length or span or, as used herein, height. Table I lists data for a non-coated airfoil, and, as discussed more below, the envelope/tolerance for the coordinates may be about +/−5% in a direction normal to any airfoil surface location and/or about +/−5% of the chord 62 in a direction nominal to any airfoil surface location. As shown in FIG. 2, the point data origin 76 is defined at or proximate to the leading edge 58 of the airfoil 52 and at or proximate to the root 64 of the airfoil 52. As will be appreciated, the point data origin 76 corresponds to the non-dimensional Z value of Table I (presented below) at Z equals 0.

The coordinate values for the X, Y and Z coordinates are set forth in non-dimensionalized units in Table I, although units of dimensions may be used when the values are appropriately converted. That is, the X, Y and Z values set forth in Table I are also expressed in non-dimensional form (X, Y, and Z) from 0% to 100% of the radial span or height of the airfoil 52. As one example, the Cartesian coordinate values of X, Y and Z may be convertible to dimensional distances by multiplying the X, Y and Z values by a height of the airfoil at the leading edge 58 and/or multiplying by a constant number. As another example, the Cartesian coordinate values of X, Y and Z may be convertible to dimensional distances by multiplying the X, Y and Z values by a height of the airfoil at the trailing edge 60 and/or multiplying by a constant number. Thus, to convert the Z value to a Z coordinate value, for example, in inches, the non-dimensional Z value given in Table I is multiplied by the height of the airfoil in inches (where the height of the airfoil is defined along the Z axis).

As described above, the Cartesian coordinate system has orthogonally-related X, Y and Z axes. The X axis lies generally parallel to the turbine rotor centerline, i.e., the rotary axis and a positive X coordinate value is axial toward an exhaust end of the turbine 14. The positive Y coordinate value extends tangentially in the direction of rotation of the rotor shaft 14, and the positive Z coordinate value extends radially outwardly toward the second end 68 of the airfoil 52. All the values in Table I are given at room temperature and are non-filleted.

By defining X and Y coordinate values at selected locations in a Z direction normal to the X, Y plane, the airfoil shape or profile sections (which may be referred to as “pressure side sections” on the pressure side and “suction side sections” on the suction side) of the airfoil 52 of the turbine nozzle 50 along the span or height of the airfoil 52 can be ascertained. Thus, by connecting the X and Y values with smooth continuing arcs, each profile section (which may include a pressure side section and suction side section) at each distance Z is determined. The airfoil profiles of the various surface locations between the distances Z can then be determined by smoothly connecting the adjacent profile sections to one another to form the airfoil profile.

The Table I values are generated and shown to four decimal places for determining the profile of the airfoil. As the turbine nozzle surface heats up during operation of the turbine 14, mechanical stresses and elevated temperatures will cause a change in the X, Y and Z values. Accordingly, it should be understood that the values for the nominal airfoil profile given in Table I represent ambient, non-operating or non-hot conditions (e.g., room temperature) and are for an uncoated airfoil.

There are typical manufacturing tolerances as well as coatings which may be accounted for in the actual profile of the airfoil 52. It will therefore be appreciated that +/− typical manufacturing tolerances, i.e., +/− values, including any coating thicknesses, may be additive to the X and Y values given in Table I below. Accordingly, a distance of +/−5% in a direction normal to any airfoil surface location and/or about +/−5% of the chord 62 in a direction nominal to any airfoil surface location may define an airfoil profile envelope for this particular airfoil design, i.e., a range of variation between measured points on the actual airfoil surface at nominal cold or room temperature and the ideal position of those points as given in Table I below at the same temperature. According to another example, a tolerance of about 10-20 percent of a thickness of the airfoil's trailing edge 60 in a direction normal to any airfoil surface location may define a range of variation between measured points on an actual airfoil surface and ideal positions as embodied by the invention in Table I. As should further be understood, the data provided in Table I is scalable and the geometry pertains to all aerodynamic scales and/or RPM ranges. The design of the airfoil 52 for the turbine nozzle 50 is robust to this range of variation without impairment of mechanical and aerodynamic functions.

TABLE I SUCTION SIDE PRESSURE SIDE X (%) Y (%) Z (%) X (%) Y (%) Z (%) 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 −0.6625 −1.8491 0.0000 0.9270 1.1284 0.0000 −0.9512 −3.7929 0.0000 1.9996 2.1185 0.0000 −0.8833 −5.7657 0.0000 3.1838 2.9751 0.0000 −0.4999 −7.6828 0.0000 4.4553 3.6934 0.0000 0.1456 −9.5392 0.0000 5.7924 4.2855 0.0000 0.9949 −11.3034 0.0000 7.1732 4.7562 0.0000 2.0093 −12.9680 0.0000 8.5904 5.1154 0.0000 3.1692 −14.5478 0.0000 10.0269 5.3726 0.0000 4.4456 −16.0353 0.0000 11.4805 5.5376 0.0000 5.8118 −17.4258 0.0000 12.9365 5.6201 0.0000 7.2533 −18.7265 0.0000 14.3973 5.6468 0.0000 8.7699 −19.9422 0.0000 15.8582 5.6371 0.0000 10.3545 −21.0803 0.0000 17.3190 5.6129 0.0000 12.0022 −22.1408 0.0000 18.7799 5.5886 0.0000 13.6960 −23.1187 0.0000 20.2407 5.5765 0.0000 15.4262 −24.0093 0.0000 21.7016 5.5910 0.0000 17.1953 −24.8101 0.0000 23.1624 5.6323 0.0000 19.0104 −25.5187 0.0000 24.6208 5.7075 0.0000 20.8692 −26.1302 0.0000 26.0768 5.8118 0.0000 22.7572 −26.6422 0.0000 27.5328 5.9477 0.0000 24.6621 −27.0426 0.0000 28.9840 6.1127 0.0000 26.5743 −27.3314 0.0000 30.4327 6.3044 0.0000 28.4938 −27.5037 0.0000 31.8765 6.5253 0.0000 30.4254 −27.5595 0.0000 33.3155 6.7752 0.0000 32.3667 −27.4940 0.0000 34.7497 7.0543 0.0000 34.3129 −27.3096 0.0000 36.1766 7.3697 0.0000 36.2542 −27.0159 0.0000 37.5962 7.7168 0.0000 38.1640 −26.6204 0.0000 39.0060 8.0977 0.0000 40.0447 −26.1302 0.0000 40.4062 8.5151 0.0000 41.9010 −25.5405 0.0000 41.7943 8.9665 0.0000 43.7332 −24.8489 0.0000 43.1726 9.4542 0.0000 45.5289 −24.0603 0.0000 44.5388 9.9760 0.0000 47.2761 −23.1867 0.0000 45.8880 10.5317 0.0000 48.9747 −22.2379 0.0000 47.2251 11.1214 0.0000 50.6249 −21.2187 0.0000 48.5452 11.7450 0.0000 52.2313 −20.1388 0.0000 49.8508 12.4026 0.0000 53.8014 −19.0007 0.0000 51.1393 13.0918 0.0000 55.3350 −17.8068 0.0000 52.4085 13.8125 0.0000 56.8322 −16.5619 0.0000 53.6630 14.5624 0.0000 58.2955 −15.2661 0.0000 54.8982 15.3413 0.0000 59.7151 −13.9290 0.0000 56.1164 16.1494 0.0000 61.0886 −12.5507 0.0000 57.3151 16.9842 0.0000 62.4136 −11.1359 0.0000 58.4945 17.8456 0.0000 63.6948 −9.6896 0.0000 59.6569 18.7313 0.0000 64.9348 −8.2094 0.0000 60.7998 19.6413 0.0000 66.1360 −6.6976 0.0000 61.9234 20.5756 0.0000 67.3057 −5.1615 0.0000 63.0275 21.5293 0.0000 68.4414 −3.6012 0.0000 64.1146 22.5048 0.0000 69.5479 −2.0165 0.0000 65.1848 23.5021 0.0000 70.6278 −0.4125 0.0000 66.2355 24.5165 0.0000 71.6834 1.2158 0.0000 67.2693 25.5502 0.0000 72.7123 2.8610 0.0000 68.2861 26.5986 0.0000 73.7193 4.5233 0.0000 69.2834 27.6639 0.0000 74.6997 6.2001 0.0000 70.2686 28.7437 0.0000 75.6607 7.8866 0.0000 71.2344 29.8406 0.0000 76.5949 9.5853 0.0000 72.1857 30.9495 0.0000 77.5098 11.2936 0.0000 73.1199 32.0707 0.0000 78.4028 13.0093 0.0000 74.0421 33.2039 0.0000 79.2764 14.7322 0.0000 74.9472 34.3517 0.0000 80.1306 16.4648 0.0000 75.8378 35.5092 0.0000 80.9653 18.2072 0.0000 76.7138 36.6789 0.0000 81.7855 19.9544 0.0000 77.5777 37.8582 0.0000 82.5888 21.7089 0.0000 78.4246 39.0473 0.0000 83.3774 23.4706 0.0000 79.2594 40.2461 0.0000 84.1564 25.2372 0.0000 80.0820 41.4545 0.0000 84.9208 27.0087 0.0000 80.8901 42.6703 0.0000 85.6755 28.7850 0.0000 81.6836 43.8958 0.0000 86.4180 30.5686 0.0000 82.4650 45.1309 0.0000 87.1509 32.3546 0.0000 83.2342 46.3709 0.0000 87.8740 34.1430 0.0000 83.9914 47.6207 0.0000 88.5874 35.9388 0.0000 84.7388 48.8777 0.0000 89.2912 37.7369 0.0000 85.4740 50.1395 0.0000 89.9876 39.5375 0.0000 86.1996 51.4087 0.0000 90.6768 41.3429 0.0000 86.9131 52.6827 0.0000 91.3587 43.1508 0.0000 87.6216 53.9615 0.0000 92.0381 44.9611 0.0000 88.3205 55.2452 0.0000 92.7103 46.7738 0.0000 89.0097 56.5313 0.0000 93.3752 48.5889 0.0000 89.6940 57.8223 0.0000 94.0377 50.4065 0.0000 90.3735 59.1157 0.0000 94.6929 52.2265 0.0000 91.0456 60.4116 0.0000 95.3433 54.0464 0.0000 91.7105 61.7122 0.0000 95.9863 55.8713 0.0000 92.3730 63.0129 0.0000 96.6270 57.6961 0.0000 93.0282 64.3185 0.0000 97.2627 59.5234 0.0000 93.6786 65.6264 0.0000 97.8961 61.3507 0.0000 94.3241 66.9393 0.0000 98.5270 63.1804 0.0000 94.9647 68.2521 0.0000 99.1580 65.0101 0.0000 95.6005 69.5673 0.0000 99.7840 66.8398 0.0000 96.2338 70.8850 0.0000 100.4101 68.6719 0.0000 96.8648 72.2027 0.0000 101.0313 70.5040 0.0000 97.4933 73.5228 0.0000 101.6477 72.3386 0.0000 98.1242 74.8404 0.0000 102.2544 74.1731 0.0000 98.7527 76.1557 0.0000 102.8562 76.0101 0.0000 99.3788 77.4709 0.0000 103.4604 77.8471 0.0000 100.0000 78.7959 0.0000 103.7759 78.7643 0.0000 100.3033 79.4669 0.0000 104.0913 79.6816 0.0000 100.6067 80.1378 0.0000 104.4675 80.8731 0.0000 101.0653 80.9629 0.0000 104.4189 82.0913 0.0000 101.8006 81.5210 0.0000 103.5041 82.8945 0.0000 102.7179 81.5550 0.0000 −2.2252 0.2038 10.0002 −3.0115 −1.1357 10.0002 −2.8440 −1.6890 10.0002 −2.2859 0.1917 10.0002 −3.0649 −3.6642 10.0002 −1.3832 1.3832 10.0002 −2.9241 −5.6565 10.0002 −0.3106 2.4436 10.0002 −2.4533 −7.5906 10.0002 0.8930 3.3561 10.0002 −1.7156 −9.4421 10.0002 2.1937 4.1156 10.0002 −0.7790 −11.1844 10.0002 3.5648 4.7490 10.0002 0.3179 −12.8370 10.0002 4.9771 5.2683 10.0002 1.5531 −14.3973 10.0002 6.4136 5.6784 10.0002 2.8926 −15.8533 10.0002 7.8721 5.9866 10.0002 4.3170 −17.2147 10.0002 9.3572 6.1928 10.0002 5.8191 −18.4911 10.0002 10.8617 6.3093 10.0002 7.3916 −19.6874 10.0002 12.3735 6.3603 10.0002 9.0296 −20.8061 10.0002 13.8853 6.3748 10.0002 10.7185 −21.8399 10.0002 15.3971 6.3772 10.0002 12.4463 −22.7839 10.0002 16.9089 6.3845 10.0002 14.2105 −23.6429 10.0002 18.4183 6.4088 10.0002 16.0135 −24.4170 10.0002 19.9277 6.4549 10.0002 17.8529 −25.1086 10.0002 21.4322 6.5301 10.0002 19.7336 −25.7104 10.0002 22.9319 6.6320 10.0002 21.6506 −26.2176 10.0002 24.4243 6.7607 10.0002 23.5919 −26.6180 10.0002 25.9142 6.9208 10.0002 25.5405 −26.9043 10.0002 27.4018 7.1077 10.0002 27.4940 −27.0790 10.0002 28.8820 7.3212 10.0002 29.4596 −27.1348 10.0002 30.3599 7.5663 10.0002 31.4373 −27.0718 10.0002 31.8304 7.8405 10.0002 33.4126 −26.8898 10.0002 33.2961 8.1487 10.0002 35.3733 −26.5986 10.0002 34.7570 8.4884 10.0002 37.3074 −26.2054 10.0002 36.2130 8.8621 10.0002 39.2123 −25.7177 10.0002 37.6641 9.2722 10.0002 41.0954 −25.1256 10.0002 39.1080 9.7188 10.0002 42.9542 −24.4316 10.0002 40.5421 10.1968 10.0002 44.7742 −23.6380 10.0002 41.9617 10.7113 10.0002 46.5457 −22.7596 10.0002 43.3643 11.2548 10.0002 48.2637 −21.8011 10.0002 44.7475 11.8324 10.0002 49.9381 −20.7746 10.0002 46.1137 12.4415 10.0002 51.5688 −19.6826 10.0002 47.4629 13.0845 10.0002 53.1583 −18.5299 10.0002 48.7952 13.7567 10.0002 54.7138 −17.3190 10.0002 50.1128 14.4629 10.0002 56.2353 −16.0547 10.0002 51.4111 15.1981 10.0002 57.7155 −14.7419 10.0002 52.6924 15.9650 10.0002 59.1497 −13.3879 10.0002 53.9591 16.7633 10.0002 60.5353 −11.9925 10.0002 55.2088 17.5908 10.0002 61.8773 −10.5608 10.0002 56.4440 18.4474 10.0002 63.1707 −9.0951 10.0002 57.6622 19.3332 10.0002 64.4252 −7.5954 10.0002 58.8658 20.2480 10.0002 65.6434 −6.0642 10.0002 60.0476 21.1847 10.0002 66.8252 −4.5039 10.0002 61.2124 22.1408 10.0002 67.9754 −2.9217 10.0002 62.3529 23.1187 10.0002 69.0966 −1.3128 10.0002 63.4740 24.1137 10.0002 70.1910 0.3179 10.0002 64.5733 25.1280 10.0002 71.2587 1.9680 10.0002 65.6531 26.1593 10.0002 72.2997 3.6400 10.0002 66.7160 27.2101 10.0002 73.3165 5.3265 10.0002 67.7595 28.2754 10.0002 74.3090 7.0227 10.0002 68.7859 29.3577 10.0002 75.2772 8.7311 10.0002 69.7930 30.4545 10.0002 76.2236 10.4492 10.0002 70.7855 31.5683 10.0002 77.1482 12.1745 10.0002 71.7634 32.6943 10.0002 78.0533 13.9120 10.0002 72.7244 33.8348 10.0002 78.9366 15.6543 10.0002 73.6732 34.9899 10.0002 79.8030 17.4088 10.0002 74.6051 36.1572 10.0002 80.6523 19.1681 10.0002 75.5248 37.3365 10.0002 81.4846 20.9347 10.0002 76.4275 38.5280 10.0002 82.3000 22.7086 10.0002 77.3205 39.7340 10.0002 83.1032 24.4898 10.0002 78.1989 40.9522 10.0002 83.8943 26.2758 10.0002 79.0628 42.1801 10.0002 84.6708 28.0667 10.0002 79.9170 43.4201 10.0002 85.4376 29.8624 10.0002 80.7542 44.6699 10.0002 86.1923 31.6630 10.0002 81.5817 45.9269 10.0002 86.9373 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17.3457 39.9985 53.8936 −13.8101 39.9985 47.4217 18.0859 39.9985 55.4418 −12.4900 39.9985 48.7952 18.8575 39.9985 56.9463 −11.1311 39.9985 50.1541 19.6608 39.9985 58.4096 −9.7260 39.9985 51.4960 20.4931 39.9985 59.8267 −8.2749 39.9985 52.8258 21.3570 39.9985 61.1978 −6.7801 39.9985 54.1411 22.2524 39.9985 62.5252 −5.2416 39.9985 55.4418 23.1770 39.9985 63.8137 −3.6667 39.9985 56.7206 24.1258 39.9985 65.0707 −2.0554 39.9985 57.9801 25.0965 39.9985 66.2962 −0.4174 39.9985 59.2152 26.0890 39.9985 67.4925 1.2400 39.9985 60.4261 27.1033 39.9985 68.6573 2.9120 39.9985 61.6152 28.1346 39.9985 69.7930 4.5985 39.9985 62.7824 29.1878 39.9985 70.8996 6.2996 39.9985 63.9278 30.2580 39.9985 71.9770 8.0152 39.9985 65.0538 31.3475 39.9985 73.0253 9.7454 39.9985 66.1627 32.4516 39.9985 74.0494 11.4878 39.9985 67.2523 33.5728 39.9985 75.0467 13.2423 39.9985 68.3249 34.7109 39.9985 76.0198 15.0064 39.9985 69.3805 35.8611 39.9985 76.9735 16.7852 39.9985 70.4239 37.0259 39.9985 77.9029 18.5712 39.9985 71.4480 38.2028 39.9985 78.8129 20.3693 39.9985 72.4575 39.3967 39.9985 79.7059 22.1748 39.9985 73.4524 40.6028 39.9985 80.5819 23.9899 39.9985 74.4303 41.8258 39.9985 81.4385 25.8123 39.9985 75.3913 43.0610 39.9985 82.2830 27.6444 39.9985 76.3353 44.3131 39.9985 83.1129 29.4814 39.9985 77.2647 45.5774 39.9985 83.9283 31.3233 39.9985 78.1771 46.8563 39.9985 84.7339 33.1748 39.9985 79.0774 48.1472 39.9985 85.5250 35.0288 39.9985 79.9631 49.4504 39.9985 86.3064 36.8900 39.9985 80.8367 50.7632 39.9985 87.0781 38.7561 39.9985 81.7006 52.0881 39.9985 87.8376 40.6270 39.9985 82.5499 53.4228 39.9985 88.5850 42.5053 39.9985 83.3896 54.7647 39.9985 89.3251 44.3859 39.9985 84.2195 56.1140 39.9985 90.0580 46.2714 39.9985 85.0372 57.4680 39.9985 90.7811 48.1594 39.9985 85.8478 58.8294 39.9985 91.4970 50.0522 39.9985 86.6461 60.1956 39.9985 92.2080 51.9474 39.9985 87.4348 61.5642 39.9985 92.9093 53.8475 39.9985 88.2137 62.9401 39.9985 93.6082 55.7500 39.9985 88.9854 64.3209 39.9985 94.2974 57.6549 39.9985 89.7498 65.7065 39.9985 94.9817 59.5598 39.9985 90.5045 67.0946 39.9985 95.6587 61.4696 39.9985 91.2519 68.4899 39.9985 96.3285 63.3818 39.9985 91.9920 69.8876 39.9985 96.9909 65.2964 39.9985 92.7225 71.2903 39.9985 97.6510 67.2110 39.9985 93.4480 72.6953 39.9985 98.3062 69.1281 39.9985 94.1663 74.1052 39.9985 98.9590 71.0452 39.9985 94.8798 75.5175 39.9985 99.6093 72.9646 39.9985 95.5908 76.9298 39.9985 100.2572 74.8817 39.9985 96.3042 78.3421 39.9985 100.9027 76.8036 39.9985 97.0176 79.7544 39.9985 101.5434 78.7255 39.9985 97.7311 81.1692 39.9985 102.1719 80.6523 39.9985 98.4421 82.5815 39.9985 102.7931 82.5790 39.9985 99.1458 83.9986 39.9985 103.4167 84.5058 39.9985 99.8326 85.4231 39.9985 103.7407 85.4668 39.9985 100.1662 86.1414 39.9985 104.0646 86.4277 39.9985 100.4999 86.8597 39.9985 104.4626 87.6726 39.9985 100.9731 87.7648 39.9985 104.4553 88.9490 39.9985 101.7205 88.4491 39.9985 103.5186 89.8056 39.9985 102.7324 88.4661 39.9985 −11.3276 1.1599 49.9988 −12.1139 −0.1796 49.9988 −11.7523 −0.8784 49.9988 −11.4659 1.3152 49.9988 −11.7062 −2.9557 49.9988 −10.5778 2.6742 49.9988 −11.2548 −4.9795 49.9988 −9.4882 3.8875 49.9988 −10.4734 −6.9014 49.9988 −8.2603 4.9382 49.9988 −9.4397 −8.6996 49.9988 −6.9135 5.8507 49.9988 −8.2215 −10.3642 49.9988 −5.4867 6.6296 49.9988 −6.8504 −11.9173 49.9988 −3.9967 7.2848 49.9988 −5.3678 −13.3636 49.9988 −2.4606 7.8235 49.9988 −3.8001 −14.6958 49.9988 −0.9003 8.2579 49.9988 −2.1646 −15.9334 49.9988 0.6746 8.6001 49.9988 −0.4611 −17.0836 49.9988 2.2616 8.8694 49.9988 1.3031 −18.1538 49.9988 3.8608 9.0708 49.9988 3.1207 −19.1414 49.9988 5.4697 9.2140 49.9988 4.9722 −20.0442 49.9988 7.0858 9.3135 49.9988 6.8504 −20.8644 49.9988 8.7068 9.3912 49.9988 8.7554 −21.6069 49.9988 10.3254 9.4712 49.9988 10.6894 −22.2670 49.9988 11.9440 9.5707 49.9988 12.6526 −22.8397 49.9988 13.5601 9.6945 49.9988 14.6473 −23.3250 49.9988 15.1739 9.8425 49.9988 16.6760 −23.7133 49.9988 16.7876 10.0148 49.9988 18.7265 −23.9972 49.9988 18.3965 10.2138 49.9988 20.7746 −24.1743 49.9988 20.0005 10.4370 49.9988 22.8154 −24.2399 49.9988 21.6021 10.6870 49.9988 24.8562 −24.1986 49.9988 23.1940 10.9636 49.9988 26.8898 −24.0627 49.9988 24.7834 11.2645 49.9988 28.9209 −23.8322 49.9988 26.3632 11.5970 49.9988 30.9495 −23.5070 49.9988 27.9405 11.9561 49.9988 32.9710 −23.0823 49.9988 29.5105 12.3468 49.9988 34.9681 −22.5582 49.9988 31.0733 12.7691 49.9988 36.9264 −21.9418 49.9988 32.6288 13.2228 49.9988 38.8483 −21.2332 49.9988 34.1770 13.7106 49.9988 40.7338 −20.4397 49.9988 35.7082 14.2299 49.9988 42.5878 −19.5613 49.9988 37.2273 14.7783 49.9988 44.4102 −18.6003 49.9988 38.7294 15.3583 49.9988 46.1962 −17.5666 49.9988 40.2145 15.9698 49.9988 47.9386 −16.4697 49.9988 41.6851 16.6129 49.9988 49.6348 −15.3170 49.9988 43.1362 17.2851 49.9988 51.2849 −14.1134 49.9988 44.5728 17.9912 49.9988 52.8962 −12.8613 49.9988 45.9924 18.7265 49.9988 54.4663 −11.5582 49.9988 47.3974 19.4933 49.9988 55.9950 −10.2065 49.9988 48.7830 20.2917 49.9988 57.4826 −8.8063 49.9988 50.1541 21.1216 49.9988 58.9289 −7.3600 49.9988 51.5082 21.9806 49.9988 60.3388 −5.8652 49.9988 52.8477 22.8712 49.9988 61.7098 −4.3292 49.9988 54.1726 23.7909 49.9988 63.0421 −2.7591 49.9988 55.4806 24.7422 49.9988 64.3330 −1.1624 49.9988 56.7716 25.7201 49.9988 65.5876 0.4562 49.9988 58.0431 26.7223 49.9988 66.8058 2.0966 49.9988 59.2929 27.7464 49.9988 67.9924 3.7565 49.9988 60.5208 28.7898 49.9988 69.1475 5.4357 49.9988 61.7268 29.8551 49.9988 70.2759 7.1344 49.9988 62.9086 30.9374 49.9988 71.3752 8.8476 49.9988 64.0734 32.0415 49.9988 72.4502 10.5778 49.9988 65.2163 33.1627 49.9988 73.4985 12.3250 49.9988 66.3399 34.3008 49.9988 74.5226 14.0843 49.9988 67.4440 35.4558 49.9988 75.5223 15.8606 49.9988 68.5311 36.6279 49.9988 76.5027 17.6491 49.9988 69.6013 37.8146 49.9988 77.4612 19.4496 49.9988 70.6569 39.0182 49.9988 78.4003 21.2648 49.9988 71.6931 40.2339 49.9988 79.3201 23.0920 49.9988 72.7147 41.4667 49.9988 80.2228 24.9290 49.9988 73.7193 42.7140 49.9988 81.1061 26.7757 49.9988 74.7094 43.9758 49.9988 81.9748 28.6321 49.9988 75.6825 45.2498 49.9988 82.8266 30.4958 49.9988 76.6435 46.5384 49.9988 83.6638 32.3667 49.9988 77.5874 47.8415 49.9988 84.4888 34.2425 49.9988 78.5168 49.1567 49.9988 85.2969 36.1232 49.9988 79.4341 50.4841 49.9988 86.0953 38.0087 49.9988 80.3368 51.8236 49.9988 86.8791 39.8991 49.9988 81.2225 53.1729 49.9988 87.6508 41.7943 49.9988 82.0961 54.5294 49.9988 88.4127 43.6943 49.9988 82.9552 55.8931 49.9988 89.1626 45.5968 49.9988 83.7997 57.2642 49.9988 89.9027 47.5042 49.9988 84.6344 58.6425 49.9988 90.6355 49.4164 49.9988 85.4595 60.0257 49.9988 91.3611 51.3286 49.9988 86.2748 61.4162 49.9988 92.0794 53.2457 49.9988 87.0805 62.8091 49.9988 92.7904 55.1651 49.9988 87.8789 64.2093 49.9988 93.4966 57.0870 49.9988 88.6700 65.6119 49.9988 94.1930 59.0114 49.9988 89.4513 67.0193 49.9988 94.8846 60.9381 49.9988 90.2254 68.4317 49.9988 95.5689 62.8673 49.9988 90.9923 69.8464 49.9988 96.2435 64.8014 49.9988 91.7518 71.2684 49.9988 96.9133 66.7354 49.9988 92.5016 72.6953 49.9988 97.5782 68.6719 49.9988 93.2466 74.1246 49.9988 98.2382 70.6108 49.9988 93.9819 75.5587 49.9988 98.8959 72.5521 49.9988 94.7147 76.9929 49.9988 99.5535 74.4910 49.9988 95.4427 78.4295 49.9988 100.2087 76.4323 49.9988 96.1707 79.8685 49.9988 100.8639 78.3737 49.9988 96.8987 81.3075 49.9988 101.5094 80.3150 49.9988 97.6267 82.7465 49.9988 102.1452 82.2636 49.9988 98.3523 84.1879 49.9988 102.7737 84.2122 49.9988 99.0657 85.6342 49.9988 103.4022 86.1632 49.9988 99.7598 87.0853 49.9988 103.7273 87.1339 49.9988 100.1128 87.8097 49.9988 104.0525 88.1045 49.9988 100.4659 88.5341 49.9988 104.4505 89.3664 49.9988 100.9707 89.4538 49.9988 104.4675 90.6598 49.9988 101.7059 90.1599 49.9988 103.5211 91.5383 49.9988 102.7348 90.1987 49.9988 −13.7494 1.4730 59.9990 −14.5357 0.1335 59.9990 −14.0333 0.1407 59.9990 −13.9144 1.6695 59.9990 −14.1086 −1.2109 59.9990 −13.0311 3.0721 59.9990 −14.0503 −1.8904 59.9990 −11.9440 4.3267 59.9990 −13.9921 −2.5698 59.9990 −10.7040 5.4211 59.9990 −13.4801 −4.5961 59.9990 −9.3426 6.3627 59.9990 −12.6307 −6.5204 59.9990 −7.8939 7.1659 59.9990 −11.5363 −8.2967 59.9990 −6.3821 7.8454 59.9990 −10.2502 −9.9493 59.9990 −4.8266 8.4108 59.9990 −8.8233 −11.4805 59.9990 −3.2396 8.8767 59.9990 −7.2969 −12.8952 59.9990 −1.6380 9.2528 59.9990 −5.6857 −14.2056 59.9990 −0.0243 9.5465 59.9990 −3.9991 −15.4238 59.9990 1.6040 9.7673 59.9990 −2.2422 −16.5571 59.9990 3.2469 9.9250 59.9990 −0.4344 −17.5981 59.9990 4.8946 10.0366 59.9990 1.4123 −18.5518 59.9990 6.5495 10.1289 59.9990 3.2881 −19.4229 59.9990 8.2021 10.2211 59.9990 5.1955 −20.2189 59.9990 9.8546 10.3278 59.9990 7.1344 −20.9347 59.9990 11.5023 10.4516 59.9990 9.1024 −21.5705 59.9990 13.1500 10.6021 59.9990 11.1092 −22.1190 59.9990 14.7929 10.7768 59.9990 13.1476 −22.5752 59.9990 16.4333 10.9806 59.9990 15.2030 −22.9295 59.9990 18.0713 11.2087 59.9990 17.2608 −23.1770 59.9990 19.7044 11.4659 59.9990 19.3186 −23.3226 59.9990 21.3351 11.7474 59.9990 21.3788 −23.3687 59.9990 22.9610 12.0532 59.9990 23.4391 −23.3177 59.9990 24.5796 12.3881 59.9990 25.5017 −23.1697 59.9990 26.1957 12.7521 59.9990 27.5668 −22.9270 59.9990 27.8022 13.1428 59.9990 29.6270 −22.5897 59.9990 29.3989 13.5626 59.9990 31.6654 −22.1578 59.9990 30.9859 14.0139 59.9990 33.6723 −21.6336 59.9990 32.5608 14.4993 59.9990 35.6451 −21.0197 59.9990 34.1212 15.0137 59.9990 37.5913 −20.3184 59.9990 35.6718 15.5597 59.9990 39.5059 −19.5273 59.9990 37.2055 16.1397 59.9990 41.3914 −18.6513 59.9990 38.7246 16.7488 59.9990 43.2478 −17.6952 59.9990 40.2291 17.3918 59.9990 45.0605 −16.6711 59.9990 41.7142 18.0640 59.9990 46.8296 −15.5888 59.9990 43.1872 18.7677 59.9990 48.5525 −14.4507 59.9990 44.6407 19.5054 59.9990 50.2342 −13.2568 59.9990 46.0797 20.2747 59.9990 51.8770 −12.0119 59.9990 47.5042 21.0755 59.9990 53.4810 −10.7137 59.9990 48.9141 21.9103 59.9990 55.0438 −9.3645 59.9990 50.3094 22.7790 59.9990 56.5677 −7.9667 59.9990 51.6902 23.6793 59.9990 58.0577 −6.5156 59.9990 53.0515 24.6087 59.9990 59.5040 −5.0207 59.9990 54.3983 25.5672 59.9990 60.9115 −3.4871 59.9990 55.7233 26.5525 59.9990 62.2752 −1.9243 59.9990 57.0264 27.5595 59.9990 63.5978 −0.3349 59.9990 58.3052 28.5908 59.9990 64.8815 1.2788 59.9990 59.5622 29.6440 59.9990 66.1288 2.9193 59.9990 60.7974 30.7166 59.9990 67.3445 4.5840 59.9990 62.0083 31.8086 59.9990 68.5263 6.2680 59.9990 63.1998 32.9200 59.9990 69.6814 7.9716 59.9990 64.3694 34.0508 59.9990 70.8073 9.6945 59.9990 65.5197 35.1986 59.9990 71.9090 11.4320 59.9990 66.6505 36.3634 59.9990 72.9841 13.1889 59.9990 67.7643 37.5452 59.9990 74.0372 14.9628 59.9990 68.8587 38.7415 59.9990 75.0661 16.7512 59.9990 69.9362 39.9549 59.9990 76.0708 18.5566 59.9990 70.9966 41.1852 59.9990 77.0560 20.3742 59.9990 72.0401 42.4301 59.9990 78.0194 22.2063 59.9990 73.0666 43.6871 59.9990 78.9633 24.0506 59.9990 74.0785 44.9611 59.9990 79.8879 25.9045 59.9990 75.0734 46.2472 59.9990 80.7930 27.7682 59.9990 76.0538 47.5503 59.9990 81.6812 29.6367 59.9990 77.0196 48.8655 59.9990 82.5499 31.5150 59.9990 77.9708 50.1929 59.9990 83.4017 33.3980 59.9990 78.9075 51.5349 59.9990 84.2389 35.2860 59.9990 79.8296 52.8889 59.9990 85.0591 37.1812 59.9990 80.7396 54.2551 59.9990 85.8672 39.0837 59.9990 81.6351 55.6311 59.9990 86.6631 40.9910 59.9990 82.5184 57.0167 59.9990 87.4469 42.9008 59.9990 83.3871 58.4120 59.9990 88.2186 44.8179 59.9990 84.2437 59.8146 59.9990 88.9781 46.7398 59.9990 85.0882 61.2221 59.9990 89.7304 48.6641 59.9990 85.9230 62.6368 59.9990 90.4705 50.5909 59.9990 86.7480 64.0564 59.9990 91.2034 52.5225 59.9990 87.5634 65.4808 59.9990 91.9289 54.4566 59.9990 88.3715 66.9101 59.9990 92.6448 56.3954 59.9990 89.1723 68.3443 59.9990 93.3558 58.3368 59.9990 89.9634 69.7833 59.9990 94.0620 60.2805 59.9990 90.7496 71.2247 59.9990 94.7584 62.2267 59.9990 91.5261 72.6710 59.9990 95.4500 64.1753 59.9990 92.2978 74.1197 59.9990 96.1343 66.1288 59.9990 93.0622 75.5733 59.9990 96.8138 68.0822 59.9990 93.8193 77.0317 59.9990 97.4860 70.0357 59.9990 94.5716 78.4926 59.9990 98.1533 71.9940 59.9990 95.3190 79.9534 59.9990 98.8182 73.9523 59.9990 96.0640 81.4191 59.9990 99.4783 75.9130 59.9990 96.8017 82.8872 59.9990 100.1359 77.8738 59.9990 97.5394 84.3554 59.9990 100.7911 79.8369 59.9990 98.2722 85.8259 59.9990 101.4414 81.8025 59.9990 99.0051 87.2965 59.9990 102.0869 83.7681 59.9990 99.7355 88.7694 59.9990 102.7227 85.7337 59.9990 100.1043 89.5023 59.9990 103.3512 87.6993 59.9990 100.4732 90.2351 59.9990 103.9943 89.6697 59.9990 100.9440 91.1912 59.9990 104.5718 91.6547 59.9990 101.7084 91.8925 59.9990 103.5259 93.2709 59.9990 102.7397 91.9314 59.9990 −16.1470 1.8321 69.9993 −16.9332 0.4926 69.9993 −16.3775 0.4975 69.9993 −16.3605 2.0772 69.9993 −16.4018 −0.8542 69.9993 −15.5039 3.5284 69.9993 −16.3180 −1.5252 69.9993 −14.4265 4.8193 69.9993 −16.2343 −2.1961 69.9993 −13.1864 5.9404 69.9993 −15.6471 −4.2030 69.9993 −11.8130 6.9160 69.9993 −14.7419 −6.0885 69.9993 −10.3521 7.7507 69.9993 −13.5917 −7.8381 69.9993 −8.8233 8.4593 69.9993 −12.2595 −9.4518 69.9993 −7.2484 9.0514 69.9993 −10.7962 −10.9491 69.9993 −5.6444 9.5416 69.9993 −9.2286 −12.3371 69.9993 −4.0258 9.9420 69.9993 −7.5784 −13.6257 69.9993 −2.3878 10.2599 69.9993 −5.8579 −14.8172 69.9993 −0.7304 10.5074 69.9993 −4.0768 −15.9189 69.9993 0.9391 10.6870 69.9993 −2.2447 −16.9308 69.9993 2.6159 10.8132 69.9993 −0.3689 −17.8602 69.9993 4.2952 10.9102 69.9993 1.5458 −18.7095 69.9993 5.9744 11.0025 69.9993 3.4895 −19.4812 69.9993 7.6561 11.1117 69.9993 5.4648 −20.1801 69.9993 9.3329 11.2427 69.9993 7.4644 −20.7964 69.9993 11.0073 11.4028 69.9993 9.4906 −21.3279 69.9993 12.6768 11.5873 69.9993 11.5363 −21.7671 69.9993 14.3415 11.7935 69.9993 13.6014 −22.1092 69.9993 16.0014 12.0265 69.9993 15.6810 −22.3495 69.9993 17.6539 12.2813 69.9993 17.7704 −22.4878 69.9993 19.3016 12.5628 69.9993 19.8646 −22.5266 69.9993 20.9420 12.8685 69.9993 21.9564 −22.4708 69.9993 22.5776 13.2010 69.9993 24.0457 −22.3204 69.9993 24.2083 13.5577 69.9993 26.1254 −22.0801 69.9993 25.8293 13.9436 69.9993 28.1929 −21.7501 69.9993 27.4455 14.3585 69.9993 30.2434 −21.3279 69.9993 29.0543 14.8050 69.9993 32.2721 −20.8158 69.9993 30.6535 15.2831 69.9993 34.2765 −20.2140 69.9993 32.2478 15.7951 69.9993 36.2542 −19.5200 69.9993 33.8324 16.3387 69.9993 38.1980 −18.7435 69.9993 35.4122 16.9162 69.9993 40.1053 −17.8844 69.9993 36.9798 17.5277 69.9993 41.9811 −16.9502 69.9993 38.5353 18.1708 69.9993 43.8181 −15.9480 69.9993 40.0762 18.8478 69.9993 45.6162 −14.8778 69.9993 41.5977 19.5540 69.9993 47.3804 −13.7494 69.9993 43.0998 20.2917 69.9993 49.1058 −12.5628 69.9993 44.5801 21.0585 69.9993 50.7899 −11.3203 69.9993 46.0409 21.8569 69.9993 52.4351 −10.0245 69.9993 47.4848 22.6844 69.9993 54.0367 −8.6777 69.9993 48.9092 23.5434 69.9993 55.5971 −7.2800 69.9993 50.3143 24.4340 69.9993 57.1162 −5.8385 69.9993 51.6999 25.3537 69.9993 58.5916 −4.3534 69.9993 53.0661 26.3001 69.9993 60.0257 −2.8295 69.9993 54.4153 27.2756 69.9993 61.4235 −1.2691 69.9993 55.7451 28.2802 69.9993 62.7800 0.3252 69.9993 57.0604 29.3116 69.9993 64.1025 1.9486 69.9993 58.3586 30.3696 69.9993 65.3886 3.6012 69.9993 59.6399 31.4543 69.9993 66.6408 5.2780 69.9993 60.9017 32.5657 69.9993 67.8614 6.9791 69.9993 62.1466 33.6965 69.9993 69.0529 8.6996 69.9993 63.3672 34.8492 69.9993 70.2152 10.4419 69.9993 64.5684 36.0188 69.9993 71.3509 12.2012 69.9993 65.7453 37.2055 69.9993 72.4599 13.9775 69.9993 66.9004 38.4067 69.9993 73.5422 15.7708 69.9993 68.0361 39.6248 69.9993 74.5978 17.5763 69.9993 69.1524 40.8576 69.9993 75.6291 19.3987 69.9993 70.2492 42.1049 69.9993 76.6362 21.2332 69.9993 71.3291 43.3667 69.9993 77.6214 23.0823 69.9993 72.3871 44.6456 69.9993 78.5872 24.9387 69.9993 73.4281 45.9390 69.9993 79.5312 26.8097 69.9993 74.4522 47.2445 69.9993 80.4557 28.6879 69.9993 75.4568 48.5622 69.9993 81.3609 30.5758 69.9993 76.4469 49.8944 69.9993 82.2466 32.4711 69.9993 77.4224 51.2388 69.9993 83.1178 34.3760 69.9993 78.3809 52.5953 69.9993 83.9695 36.2882 69.9993 79.3249 53.9639 69.9993 84.8067 38.2052 69.9993 80.2543 55.3423 69.9993 85.6318 40.1320 69.9993 81.1692 56.7328 69.9993 86.4399 42.0612 69.9993 82.0695 58.1354 69.9993 87.2382 43.9977 69.9993 82.9576 59.5452 69.9993 88.0245 45.9366 69.9993 83.8336 60.9673 69.9993 88.8010 47.8827 69.9993 84.6999 62.3966 69.9993 89.5654 49.8313 69.9993 85.5566 63.8331 69.9993 90.3201 51.7848 69.9993 86.4035 65.2770 69.9993 91.0651 53.7407 69.9993 87.2431 66.7257 69.9993 91.8003 55.7014 69.9993 88.0706 68.1793 69.9993 92.5259 57.6646 69.9993 88.8908 69.6377 69.9993 93.2442 59.6302 69.9993 89.7013 71.1010 69.9993 93.9576 61.6006 69.9993 90.5069 72.5667 69.9993 94.6614 63.5711 69.9993 91.3029 74.0397 69.9993 95.3602 65.5464 69.9993 92.0915 75.5151 69.9993 96.0543 67.5217 69.9993 92.8753 76.9929 69.9993 96.7410 69.4970 69.9993 93.6494 78.4756 69.9993 97.4253 71.4747 69.9993 94.4187 79.9631 69.9993 98.1048 73.4573 69.9993 95.1782 81.4531 69.9993 98.7770 75.4398 69.9993 95.9329 82.9455 69.9993 99.4419 77.4224 69.9993 96.6876 84.4379 69.9993 100.1019 79.4123 69.9993 97.4447 85.9327 69.9993 100.7547 81.4021 69.9993 98.2043 87.4227 69.9993 101.4026 83.3920 69.9993 98.9614 88.9175 69.9993 102.0505 85.3843 69.9993 99.7015 90.4171 69.9993 102.6984 87.3741 69.9993 100.0631 91.1694 69.9993 103.3512 89.3615 69.9993 100.4247 91.9217 69.9993 104.0040 91.3514 69.9993 100.9294 92.8850 69.9993 104.5645 93.3752 69.9993 101.6792 93.6325 69.9993 103.5284 95.0059 69.9993 102.7421 93.6664 69.9993 −18.4450 2.2058 79.9995 −19.2312 0.8663 79.9995 −18.6391 0.8372 79.9995 −18.6925 2.4995 79.9995 −18.6100 −0.5581 79.9995 −17.8553 3.9894 79.9995 −18.4972 −1.2437 79.9995 −16.7755 5.3289 79.9995 −18.3843 −1.9292 79.9995 −15.5282 6.4913 79.9995 −17.6927 −3.9676 79.9995 −14.1450 7.5008 79.9995 −16.6857 −5.8555 79.9995 −12.6623 8.3671 79.9995 −15.4359 −7.6027 79.9995 −11.1141 9.1048 79.9995 −14.0115 −9.2043 79.9995 −9.5173 9.7333 79.9995 −12.4706 −10.6749 79.9995 −7.8866 10.2550 79.9995 −10.8277 −12.0338 79.9995 −6.2389 10.6773 79.9995 −9.0927 −13.2956 79.9995 −4.5742 11.0194 79.9995 −7.2969 −14.4556 79.9995 −2.8950 11.2888 79.9995 −5.4551 −15.5185 79.9995 −1.2012 11.4902 79.9995 −3.5696 −16.4891 79.9995 0.4999 11.6358 79.9995 −1.6428 −17.3748 79.9995 2.2083 11.7523 79.9995 0.3179 −18.1853 79.9995 3.9166 11.8615 79.9995 2.3126 −18.9231 79.9995 5.6250 11.9804 79.9995 4.3437 −19.5880 79.9995 7.3309 12.1211 79.9995 6.3991 −20.1704 79.9995 9.0344 12.2886 79.9995 8.4642 −20.6654 79.9995 10.7355 12.4851 79.9995 10.5414 −21.0658 79.9995 12.4318 12.7060 79.9995 12.6307 −21.3715 79.9995 14.1256 12.9511 79.9995 14.7322 −21.5827 79.9995 15.8145 13.2180 79.9995 16.8458 −21.6943 79.9995 17.4986 13.5092 79.9995 18.9740 −21.7064 79.9995 19.1778 13.8222 79.9995 21.1119 −21.6239 79.9995 20.8522 14.1620 79.9995 23.2401 −21.4468 79.9995 22.5218 14.5308 79.9995 25.3488 −21.1847 79.9995 24.1865 14.9239 79.9995 27.4382 −20.8377 79.9995 25.8439 15.3486 79.9995 29.5105 −20.4009 79.9995 27.4964 15.8024 79.9995 31.5635 −19.8719 79.9995 29.1344 16.2853 79.9995 33.5970 −19.2506 79.9995 30.7603 16.8022 79.9995 35.6087 −18.5348 79.9995 32.3716 17.3482 79.9995 37.5962 −17.7340 79.9995 33.9683 17.9257 79.9995 39.5399 −16.8555 79.9995 35.5481 18.5324 79.9995 41.4400 −15.9043 79.9995 37.1157 19.1681 79.9995 43.3036 −14.8851 79.9995 38.6663 19.8355 79.9995 45.1285 −13.7980 79.9995 40.2048 20.5343 79.9995 46.9169 −12.6501 79.9995 41.7263 21.2648 79.9995 48.6714 −11.4392 79.9995 43.2333 22.0267 79.9995 50.3895 −10.1677 79.9995 44.7257 22.8203 79.9995 52.0663 −8.8452 79.9995 46.2011 23.6477 79.9995 53.6994 −7.4789 79.9995 47.6619 24.5044 79.9995 55.2816 −6.0691 79.9995 49.1058 25.3949 79.9995 56.8128 −4.6131 79.9995 50.5327 26.3195 79.9995 58.3004 −3.1134 79.9995 51.9474 27.2780 79.9995 59.7442 −1.5749 79.9995 53.3451 28.2657 79.9995 61.1517 0.0000 79.9995 54.7235 29.2824 79.9995 62.5203 1.6064 79.9995 56.0776 30.3210 79.9995 63.8574 3.2444 79.9995 57.4074 31.3839 79.9995 65.1605 4.9115 79.9995 58.7129 32.4662 79.9995 66.4345 6.6102 79.9995 59.9966 33.5703 79.9995 67.6794 8.3331 79.9995 61.2585 34.6963 79.9995 68.8927 10.0803 79.9995 62.4961 35.8393 79.9995 70.0769 11.8445 79.9995 63.7167 37.0041 79.9995 71.2296 13.6232 79.9995 64.9130 38.1858 79.9995 72.3507 15.4165 79.9995 66.0924 39.3870 79.9995 73.4427 17.2220 79.9995 67.2523 40.6052 79.9995 74.5080 19.0395 79.9995 68.3928 41.8404 79.9995 75.5466 20.8668 79.9995 69.5139 43.0925 79.9995 76.5609 22.7086 79.9995 70.6181 44.3617 79.9995 77.5510 24.5602 79.9995 71.7076 45.6454 79.9995 78.5193 26.4214 79.9995 72.7778 46.9436 79.9995 79.4657 28.2924 79.9995 73.8310 48.2589 79.9995 80.3926 30.1730 79.9995 74.8671 49.5911 79.9995 81.3002 32.0610 79.9995 75.8863 50.9379 79.9995 82.1884 33.9586 79.9995 76.8861 52.3017 79.9995 83.0620 35.8635 79.9995 77.8713 53.6800 79.9995 83.9186 37.7733 79.9995 78.8396 55.0753 79.9995 84.7606 39.6928 79.9995 79.7957 56.4804 79.9995 85.5857 41.6195 79.9995 80.7372 57.8951 79.9995 86.3986 43.5487 79.9995 81.6691 59.3220 79.9995 87.1994 45.4876 79.9995 82.5888 60.7537 79.9995 87.9881 47.4290 79.9995 83.4939 62.1952 79.9995 88.7646 49.3776 79.9995 84.3869 63.6439 79.9995 89.5314 51.3310 79.9995 85.2654 65.0999 79.9995 90.2885 53.2869 79.9995 86.1341 66.5631 79.9995 91.0359 55.2476 79.9995 86.9907 68.0313 79.9995 91.7736 57.2132 79.9995 87.8352 69.5042 79.9995 92.5041 59.1812 79.9995 88.6724 70.9845 79.9995 93.2272 61.1541 79.9995 89.4999 72.4696 79.9995 93.9431 63.1318 79.9995 90.3201 73.9596 79.9995 94.6492 65.1096 79.9995 91.1282 75.4544 79.9995 95.3505 67.0921 79.9995 91.9289 76.9565 79.9995 96.0470 69.0771 79.9995 92.7225 78.4610 79.9995 96.7337 71.0646 79.9995 93.5063 79.9680 79.9995 97.4180 73.0569 79.9995 94.2852 81.4798 79.9995 98.0926 75.0491 79.9995 95.0618 82.9940 79.9995 98.7648 77.0438 79.9995 95.8359 84.5082 79.9995 99.4322 79.0410 79.9995 96.6124 86.0225 79.9995 100.0946 81.0381 79.9995 97.3913 87.5367 79.9995 100.7547 83.0377 79.9995 98.1679 89.0509 79.9995 101.4099 85.0372 79.9995 98.9323 90.5700 79.9995 102.0627 87.0392 79.9995 99.6748 92.0988 79.9995 102.7081 89.0437 79.9995 100.0449 92.8644 79.9995 103.3464 91.0505 79.9995 100.4150 93.6300 79.9995 103.9821 93.0549 79.9995 100.9294 94.6080 79.9995 104.5742 95.0739 79.9995 101.6647 95.3724 79.9995 103.5308 96.7386 79.9995 102.7445 95.3991 79.9995 −20.7042 2.6038 89.9998 −21.4905 1.2643 89.9998 −20.8474 0.4417 89.9998 −20.9711 2.9314 89.9998 −20.4785 −1.6962 89.9998 −20.1437 4.4602 89.9998 −19.6923 −3.7201 89.9998 −19.0614 5.8313 89.9998 −18.5979 −5.5862 89.9998 −17.8044 7.0276 89.9998 −17.2705 −7.3018 89.9998 −16.4139 8.0711 89.9998 −15.7878 −8.8646 89.9998 −14.9191 8.9738 89.9998 −14.1814 −10.3011 89.9998 −13.3587 9.7479 89.9998 −12.4682 −11.6261 89.9998 −11.7426 10.4103 89.9998 −10.6846 −12.8443 89.9998 −10.0973 10.9661 89.9998 −8.8476 −13.9581 89.9998 −8.4302 11.4247 89.9998 −6.9645 −14.9773 89.9998 −6.7461 11.7911 89.9998 −5.0353 −15.9140 89.9998 −5.0426 12.0847 89.9998 −3.0649 −16.7706 89.9998 −3.3269 12.3153 89.9998 −1.0556 −17.5544 89.9998 −1.5992 12.4924 89.9998 0.9828 −18.2679 89.9998 0.1335 12.6356 89.9998 3.0382 −18.9012 89.9998 1.8685 12.7642 89.9998 5.1105 −19.4545 89.9998 3.6012 12.9025 89.9998 7.1999 −19.9253 89.9998 5.3338 13.0627 89.9998 9.3062 −20.3087 89.9998 7.0616 13.2447 89.9998 11.4295 −20.6023 89.9998 8.7869 13.4534 89.9998 13.5747 −20.8061 89.9998 10.5098 13.6888 89.9998 15.7344 −20.9129 89.9998 12.2303 13.9460 89.9998 17.8869 −20.9153 89.9998 13.9436 14.2250 89.9998 20.0296 −20.8255 89.9998 15.6543 14.5235 89.9998 22.1578 −20.6484 89.9998 17.3603 14.8463 89.9998 24.2763 −20.3936 89.9998 19.0589 15.1933 89.9998 26.3850 −20.0587 89.9998 20.7552 15.5646 89.9998 28.4792 −19.6268 89.9998 22.4466 15.9625 89.9998 30.5613 −19.0953 89.9998 24.1307 16.3896 89.9998 32.6288 −18.4693 89.9998 25.8099 16.8458 89.9998 34.6672 −17.7534 89.9998 27.4770 17.3312 89.9998 36.6667 −16.9599 89.9998 29.1320 17.8480 89.9998 38.6251 −16.0887 89.9998 30.7724 18.3965 89.9998 40.5470 −15.1423 89.9998 32.3958 18.9716 89.9998 42.4325 −14.1256 89.9998 34.0071 19.5782 89.9998 44.2840 −13.0384 89.9998 35.6039 20.2140 89.9998 46.1016 −11.8809 89.9998 37.1861 20.8814 89.9998 47.8827 −10.6627 89.9998 38.7537 21.5778 89.9998 49.6251 −9.3912 89.9998 40.3067 22.3058 89.9998 51.3237 −8.0759 89.9998 41.8452 23.0629 89.9998 52.9787 −6.7194 89.9998 43.3692 23.8516 89.9998 54.5852 −5.3144 89.9998 44.8761 24.6742 89.9998 56.1406 −3.8535 89.9998 46.3685 25.5260 89.9998 57.6452 −2.3417 89.9998 47.8463 26.4117 89.9998 59.1084 −0.7887 89.9998 49.3072 27.3290 89.9998 60.5353 0.8008 89.9998 50.7535 28.2802 89.9998 61.9331 2.4194 89.9998 52.1852 29.2655 89.9998 63.2969 4.0744 89.9998 53.5975 30.2774 89.9998 64.6315 5.7609 89.9998 54.9904 31.3184 89.9998 65.9322 7.4741 89.9998 56.3590 32.3813 89.9998 67.1989 9.2067 89.9998 57.7010 33.4660 89.9998 68.4317 10.9563 89.9998 59.0211 34.5725 89.9998 69.6304 12.7254 89.9998 60.3145 35.7009 89.9998 70.7976 14.5065 89.9998 61.5885 36.8512 89.9998 71.9333 16.3071 89.9998 62.8431 38.0184 89.9998 73.0399 18.1198 89.9998 64.0758 39.2050 89.9998 74.1197 19.9447 89.9998 65.2867 40.4111 89.9998 75.1753 21.7865 89.9998 66.4758 41.6365 89.9998 76.2042 23.6380 89.9998 67.6454 42.8814 89.9998 77.2089 25.5041 89.9998 68.7981 44.1408 89.9998 78.1917 27.3799 89.9998 69.9313 45.4173 89.9998 79.1550 29.2655 89.9998 71.0524 46.7058 89.9998 80.0966 31.1607 89.9998 72.1590 48.0089 89.9998 81.0211 33.0680 89.9998 73.2461 49.3290 89.9998 81.9263 34.9826 89.9998 74.3139 50.6661 89.9998 82.8144 36.9046 89.9998 75.3573 52.0250 89.9998 83.6880 38.8362 89.9998 76.3814 53.4034 89.9998 84.5446 40.7775 89.9998 77.3860 54.7987 89.9998 85.3843 42.7237 89.9998 78.3761 56.2086 89.9998 86.2142 44.6771 89.9998 79.3516 57.6306 89.9998 87.0271 46.6379 89.9998 80.3174 59.0648 89.9998 87.8303 48.6035 89.9998 81.2711 60.5062 89.9998 88.6214 50.5763 89.9998 82.2126 61.9573 89.9998 89.4028 52.5541 89.9998 83.1420 63.4158 89.9998 90.1720 54.5391 89.9998 84.0569 64.8815 89.9998 90.9316 56.5265 89.9998 84.9596 66.3544 89.9998 91.6839 58.5212 89.9998 85.8502 67.8371 89.9998 92.4240 60.5183 89.9998 86.7286 69.3247 89.9998 93.1568 62.5179 89.9998 87.5925 70.8195 89.9998 93.8824 64.5223 89.9998 88.4491 72.3192 89.9998 94.6007 66.5292 89.9998 89.2912 73.8261 89.9998 95.3093 68.5384 89.9998 90.1259 75.3379 89.9998 96.0130 70.5501 89.9998 90.9510 76.8570 89.9998 96.7095 72.5618 89.9998 91.7664 78.3785 89.9998 97.4011 74.5784 89.9998 92.5720 79.9073 89.9998 98.0829 76.5973 89.9998 93.3704 81.4385 89.9998 98.7600 78.6163 89.9998 94.1663 82.9746 89.9998 99.4322 80.6402 89.9998 94.9550 84.5107 89.9998 100.0995 82.6640 89.9998 95.7461 86.0467 89.9998 100.7620 84.6878 89.9998 96.5396 87.5828 89.9998 101.4244 86.7141 89.9998 97.3331 89.1165 89.9998 102.0796 88.7428 89.9998 98.1242 90.6525 89.9998 102.7276 90.7714 89.9998 98.9032 92.1959 89.9998 103.3633 92.8050 89.9998 99.6578 93.7489 89.9998 103.6861 93.8217 89.9998 100.0303 94.5291 89.9998 104.0088 94.8385 89.9998 100.4028 95.3093 89.9998 104.4359 96.1465 89.9998 100.9100 96.3066 89.9998 104.5039 97.5078 89.9998 101.6477 97.0953 89.9998 103.5332 98.4664 89.9998 102.7470 97.1268 89.9998 −22.9295 2.9993 100.0000 −23.7157 1.6598 100.0000 −23.0289 0.8081 100.0000 −23.2279 3.3512 100.0000 −22.5897 −1.3444 100.0000 −22.4102 4.9140 100.0000 −21.7380 −3.3633 100.0000 −21.3400 6.3214 100.0000 −20.5780 −5.2222 100.0000 −20.0733 7.5590 100.0000 −19.1876 −6.9184 100.0000 −18.6755 8.6389 100.0000 −17.6491 −8.4545 100.0000 −17.1831 9.5707 100.0000 −15.9795 −9.8692 100.0000 −15.6131 10.3812 100.0000 −14.2129 −11.1626 100.0000 −13.9872 11.0777 100.0000 −12.3808 −12.3444 100.0000 −12.3226 11.6674 100.0000 −10.4977 −13.4243 100.0000 −10.6239 12.1600 100.0000 −8.5685 −14.4143 100.0000 −8.9010 12.5652 100.0000 −6.5956 −15.3195 100.0000 −7.1659 12.8880 100.0000 −4.5815 −16.1470 100.0000 −5.4260 13.1428 100.0000 −2.5334 −16.9041 100.0000 −3.6788 13.3442 100.0000 −0.4611 −17.5860 100.0000 −1.9243 13.5140 100.0000 1.6283 −18.1951 100.0000 −0.1699 13.6645 100.0000 3.7322 −18.7216 100.0000 1.5846 13.8222 100.0000 5.8555 −19.1706 100.0000 3.3366 13.9945 100.0000 7.9958 −19.5394 100.0000 5.0863 14.1935 100.0000 10.1531 −19.8233 100.0000 6.8335 14.4143 100.0000 12.3274 −20.0175 100.0000 8.5734 14.6570 100.0000 14.5090 −20.1170 100.0000 10.3109 14.9215 100.0000 16.6784 −20.1145 100.0000 12.0459 15.2078 100.0000 18.8357 −20.0199 100.0000 13.7737 15.5136 100.0000 20.9833 −19.8476 100.0000 15.4966 15.8436 100.0000 23.1236 −19.6025 100.0000 17.2147 16.1955 100.0000 25.2542 −19.2773 100.0000 18.9279 16.5716 100.0000 27.3727 −18.8527 100.0000 20.6338 16.9720 100.0000 29.4814 −18.3237 100.0000 22.3349 17.4015 100.0000 31.5756 −17.7024 100.0000 24.0312 17.8602 100.0000 33.6431 −16.9939 100.0000 25.7201 18.3479 100.0000 35.6694 −16.2052 100.0000 27.3994 18.8672 100.0000 37.6592 −15.3413 100.0000 29.0713 19.4157 100.0000 39.6103 −14.3998 100.0000 30.7312 19.9956 100.0000 41.5249 −13.3879 100.0000 32.3788 20.6047 100.0000 43.4031 −12.3007 100.0000 34.0071 21.2405 100.0000 45.2498 −11.1481 100.0000 35.6209 21.9078 100.0000 47.0625 −9.9299 100.0000 37.2176 22.6019 100.0000 48.8364 −8.6583 100.0000 38.8022 23.3250 100.0000 50.5642 −7.3406 100.0000 40.3674 24.0797 100.0000 52.2483 −5.9793 100.0000 41.9205 24.8635 100.0000 53.8814 −4.5670 100.0000 43.4541 25.6764 100.0000 55.4636 −3.0988 100.0000 44.9732 26.5209 100.0000 56.9948 −1.5798 100.0000 46.4753 27.3969 100.0000 58.4799 −0.0146 100.0000 47.9604 28.3021 100.0000 59.9287 1.5870 100.0000 49.4285 29.2412 100.0000 61.3458 3.2202 100.0000 50.8821 30.2094 100.0000 62.7339 4.8873 100.0000 52.3187 31.2068 100.0000 64.0928 6.5835 100.0000 53.7383 32.2381 100.0000 65.4177 8.3040 100.0000 55.1433 33.2961 100.0000 66.7112 10.0488 100.0000 56.5289 34.3833 100.0000 67.9657 11.8130 100.0000 57.8927 35.4947 100.0000 69.1863 13.5917 100.0000 59.2322 36.6279 100.0000 70.3730 15.3898 100.0000 60.5499 37.7806 100.0000 71.5305 17.2026 100.0000 61.8433 38.9551 100.0000 72.6565 19.0298 100.0000 63.1149 40.1490 100.0000 73.7533 20.8741 100.0000 64.3670 41.3623 100.0000 74.8259 22.7305 100.0000 65.5949 42.5975 100.0000 75.8718 24.5990 100.0000 66.8058 43.8521 100.0000 76.8934 26.4821 100.0000 67.9949 45.1212 100.0000 77.8932 28.3749 100.0000 69.1694 46.4073 100.0000 78.8711 30.2774 100.0000 70.3269 47.7056 100.0000 79.8272 32.1920 100.0000 71.4723 49.0184 100.0000 80.7663 34.1163 100.0000 72.5958 50.3507 100.0000 81.6885 36.0504 100.0000 73.6975 51.7023 100.0000 82.5912 37.9917 100.0000 74.7749 53.0782 100.0000 83.4769 39.9427 100.0000 75.8281 54.4735 100.0000 84.3481 41.9010 100.0000 76.8643 55.8883 100.0000 85.2023 43.8666 100.0000 77.8810 57.3151 100.0000 86.0443 45.8419 100.0000 78.8857 58.7590 100.0000 86.8718 47.8221 100.0000 79.8782 60.2101 100.0000 87.6872 49.8071 100.0000 80.8537 61.6710 100.0000 88.4904 51.8018 100.0000 81.8171 63.1415 100.0000 89.2815 53.8014 100.0000 82.7659 64.6194 100.0000 90.0629 55.8058 100.0000 83.7002 66.1045 100.0000 90.8321 57.8150 100.0000 84.6247 67.5969 100.0000 91.5916 59.8292 100.0000 85.5347 69.0966 100.0000 92.3415 61.8481 100.0000 86.4350 70.6035 100.0000 93.0840 63.8720 100.0000 87.3232 72.1153 100.0000 93.8169 65.8982 100.0000 88.1968 73.6368 100.0000 94.5425 67.9269 100.0000 89.0606 75.1632 100.0000 95.2607 69.9580 100.0000 89.9124 76.6968 100.0000 95.9718 71.9916 100.0000 90.7544 78.2378 100.0000 96.6731 74.0275 100.0000 91.5868 79.7811 100.0000 97.3671 76.0659 100.0000 92.4119 81.3317 100.0000 98.0562 78.1067 100.0000 93.2296 82.8848 100.0000 98.7381 80.1500 100.0000 94.0401 84.4403 100.0000 99.4127 82.1956 100.0000 94.8482 86.0006 100.0000 100.0849 84.2437 100.0000 95.6514 87.5634 100.0000 100.7547 86.2894 100.0000 96.4522 89.1262 100.0000 101.4196 88.3399 100.0000 97.2555 90.6889 100.0000 102.0796 90.3904 100.0000 98.0611 92.2468 100.0000 102.7276 92.4458 100.0000 98.8643 93.8072 100.0000 103.3658 94.5036 100.0000 99.6433 95.3797 100.0000 103.6922 95.5301 100.0000 100.0085 96.1817 100.0000 104.0185 96.5566 100.0000 100.3737 96.9837 100.0000 104.4432 97.8815 100.0000 100.8784 97.9980 100.0000 104.4990 99.2477 100.0000 101.6307 98.8255 100.0000 103.5356 100.1990 100.0000 102.7494 98.8595 100.0000

It will also be appreciated that the airfoil 52 disclosed in the above Table I may be scaled up or down geometrically for use in other similar turbine designs. Consequently, the coordinate values set forth in Table I may be scaled upwardly or downwardly such that the airfoil profile shape remains unchanged. A scaled version of the coordinates in Table I would be represented by X, Y and Z coordinate values of Table I, with the X, Y and Z non-dimensional coordinate values converted to inches, multiplied or divided by a constant number.

An important term in this disclosure is “profile”. The profile is the range of the variation between measured points on an airfoil surface and the ideal position listed in Table I. The actual profile on a manufactured turbine nozzle will be different than those in Table I and the design is robust to this variation meaning that mechanical and aerodynamic function are not impaired. As noted above, a + or −5% profile tolerance is used herein. The X, Y and Z values are all non-dimensionalized relative to the airfoil height.

The disclosed airfoil shape optimizes and is specific to the machine conditions and specifications. It provides a unique profile to achieve 1) interaction between other stages in the turbine 10; 2) aerodynamic efficiency; and 3) normalized aerodynamic and mechanical nozzle or airfoil loadings. The disclosed locus of points defined in Table I allow the gas turbine 12 or any other suitable turbine to run in an efficient, safe and smooth manner. As also noted, any scale of the disclosed airfoil 52 may be adopted as long as 1) interaction between other stages in the pressure turbine 10; 2) aerodynamic efficiency; and 3) normalized aerodynamic and mechanical nozzle or airfoil loadings are maintained in the scaled turbine. The airfoil 52 described herein thus improves overall gas turbine 12 efficiency. Specifically, the airfoil 52 provides a desired turbine efficiency lapse rate (ISO, hot, cold, part load, etc.). The airfoil 52 also meets all aeromechanics and stress requirements. The turbine nozzle 50 described herein has very specific aerodynamic design requirements such as an upstream bucket radial back pressure (i.e., work splits) and radial velocity triangles for the downstream turbine rotors 150, 250, 350 and 450. Significant cross-functional design effort was required to meet these design goals. The airfoil 52 of the turbine nozzle 50, thus, is of a specific shape to meet aerodynamic, mechanical, and heat transfer requirements in an efficient and cost-effective manner.

Further, it should be understood that exemplary embodiments of the present disclosure may include the entirety of the nominal airfoil profile set forth in Table I or portions thereof. Such portions may include a portion of the pressure side (or “pressure side portion”), a portion of the suction side (or “suction side portion”), and portions of both the pressure side and suction side.

Thus, exemplary embodiments of the present disclosure include a turbine nozzle having an airfoil that includes a pressure side portion of a nominal airfoil profile substantially in accordance with Cartesian coordinate values of X, Y, and Z of a pressure side as set forth in Table I. The Cartesian coordinate values of X, Y, and Z are non-dimensional values from 0% to 100% convertible to dimensional distances by multiplying the Cartesian coordinate values of X, Y and Z by a height of the airfoil defined along the Z axis. The X and Y values of the pressure side are coordinate values that, when connected by smooth continuing arcs, define pressure side sections of the pressure side portion of the nominal airfoil profile at each Z coordinate value. The pressure side sections may be joined smoothly with one another to form the pressure side portion.

Exemplary embodiments of the present disclosure also include a turbine nozzle having an airfoil that includes a suction side portion of a nominal airfoil profile substantially in accordance with Cartesian coordinate values of X, Y, and Z of a suction side as set forth in Table I. The Cartesian coordinate values of X, Y, and Z are non-dimensional values from 0% to 100% convertible to dimensional distances by multiplying the Cartesian coordinate values of X, Y and Z by a height of the airfoil defined along the Z axis. The X and Y values of the suction side are coordinate values that, when connected by smooth continuing arcs, define suction side sections of the suction side portion of the nominal airfoil profile at each Z coordinate value. The suction side sections may be joined smoothly with one another to form the suction side portion.

Exemplary embodiment of the present disclosure also include a turbine engine that has an airfoil, wherein the airfoil includes: a pressure side portion of a nominal airfoil profile substantially in accordance with Cartesian coordinate values of X, Y, and Z of a pressure side as set forth in Table I; and a suction side portion of the nominal airfoil profile substantially in accordance with Cartesian coordinate values of X, Y, and Z of the suction side as set forth in Table I. The Cartesian coordinate values of X, Y, and Z are non-dimensional values from 0% to 100% convertible to dimensional distances by multiplying the Cartesian coordinate values of X, Y and Z by a height of the airfoil defined along the Z axis. The X and Y values of the pressure side are coordinate values that, when connected by smooth continuing arcs, define pressure side sections of the pressure side portion of the nominal airfoil profile at each Z coordinate value. The pressure side sections may be joined smoothly with one another to form the pressure side portion. The X and Y values of the suction side are coordinate values that, when connected by smooth continuing arcs, define suction side sections of the suction side portion of the nominal airfoil profile at each Z coordinate value. The suction side sections may be joined smoothly with one another to form the suction side portion.

A height of each of the suction side portion and pressure side portion may be defined along the Z axis. The height of each of the suction side portion and pressure side portion may be less than or equal to the height of the airfoil. According to exemplary embodiments, the height of the suction side portion and the height of the pressure side portion may be substantially the same. According to exemplary embodiments, the suction side portion and the pressure side portion may each start at a common distance relative to a base of the airfoil and extend toward a tip of the airfoil. According to exemplary embodiments, the height of the suction side portion and/or the height of the pressure side portion may each be equal to or greater than 50% of the height of the airfoil. According to other embodiments, the height of the suction side portion and/or the height of the pressure side portion may each be equal to or greater than 75% of the height of the airfoil. According to other embodiments, the height of the suction side portion and the height of the pressure side portion may each be equal to 100% of the height of the airfoil.

As already described, the turbine engine may include a combustion or gas turbine that has a compressor, combustor, and turbine. The airfoil of the present disclosure may be configured as the airfoil of a turbine nozzle, i.e., a nozzle within the turbine of the gas turbine. More specifically, the airfoil of the present disclosure may be the airfoil of a turbine nozzle that is configured to function as a second stage nozzle in the turbine. In such cases, the turbine includes a second stage that has a row of circumferentially spaced nozzles and a row of circumferentially spaced rotor blades, with the airfoil of the present disclosure being configured as the airfoil of each of the nozzles within the second stage row of nozzles.

This written description uses examples to disclose the invention, including the best mode, and also to enable any person skilled in the art to practice the invention, including making and using any devices or systems and performing any incorporated methods. The patentable scope of the invention is defined by the claims, and may include other examples that occur to those skilled in the art. Such other examples are intended to be within the scope of the claims if they have structural elements that do not differ from the literal language of the claims, or if they include equivalent structural elements with insubstantial differences from the literal languages of the claims. 

What is claimed:
 1. A turbine nozzle including an airfoil that comprises a pressure side portion of a nominal airfoil profile substantially in accordance with Cartesian coordinate values of X, Y, and Z of a pressure side as set forth in Table I, wherein: the Cartesian coordinate values of X, Y, and Z are non-dimensional values from 0% to 100% convertible to dimensional distances by multiplying the Cartesian coordinate values of X, Y and Z by a height of the airfoil defined along a Z axis; the X and Y values of the pressure side are coordinate values that, when connected by smooth continuing arcs, define pressure side sections of the pressure side portion of the nominal airfoil profile at each Z coordinate value; and the pressure side sections are joined smoothly with one another to form the pressure side portion.
 2. The turbine nozzle of claim 1, wherein the nominal airfoil profile lies in an envelope within +/−5% of a chord length in a direction normal to any of the pressure side sections.
 3. The turbine nozzle of claim 1, wherein a height of the pressure side portion is defined along the Z axis, and wherein the height of the pressure side portion is less than or equal to the height of the airfoil.
 4. The turbine nozzle of claim 3, wherein the height of the pressure side portion is equal to or greater than 50% of the height of the airfoil; and wherein the height of the airfoil is between 3 and 10 inches.
 5. The turbine nozzle of claim 3, wherein the height of the pressure side portion is equal to or greater than 75% of the height of the airfoil; and wherein the turbine nozzle is configured to function as a second stage turbine nozzle in a turbine.
 6. The turbine nozzle of claim 3, wherein the height of the pressure side portion is equal to 100% of the height of the airfoil.
 7. A turbine nozzle including an airfoil that comprises a suction side portion of a nominal airfoil profile substantially in accordance with Cartesian coordinate values of X, Y, and Z of a suction side as set forth in Table I, wherein: the Cartesian coordinate values of X, Y, and Z are non-dimensional values from 0% to 100% convertible to dimensional distances by multiplying the Cartesian coordinate values of X, Y and Z by a height of the airfoil defined along a Z axis; the X and Y values of the suction side are coordinate values that, when connected by smooth continuing arcs, define suction side sections of the suction side portion of the nominal airfoil profile at each Z coordinate value; and the suction side sections are joined smoothly with one another to form the suction side portion.
 8. The turbine nozzle of claim 7, wherein the nominal airfoil profile lies in an envelope within +/−5% of a chord length in a direction normal to any of the suction side sections.
 9. The turbine nozzle of claim 7, wherein a height of the suction side portion is defined along the Z axis, and wherein the height of the suction side portion is less than or equal to the height of the airfoil.
 10. The turbine nozzle of claim 9, wherein the height of the suction side portion is equal to or greater than 50% of the height of the airfoil; and wherein the height of the airfoil is between 3 and 10 inches.
 11. The turbine nozzle of claim 9, wherein the height of the suction side portion is equal to or greater than 75% of the height of the airfoil; and wherein the turbine nozzle is configured to function as a second stage turbine nozzle in a turbine.
 12. The turbine nozzle of claim 9, wherein the height of the suction side portion is equal to 100% of the height of the airfoil.
 13. A turbine engine that includes an airfoil that comprises: a pressure side portion of a nominal airfoil profile substantially in accordance with Cartesian coordinate values of X, Y, and Z of a pressure side as set forth in Table I; a suction side portion of the nominal airfoil profile substantially in accordance with Cartesian coordinate values of X, Y, and Z of the suction side as set forth in Table I wherein: the Cartesian coordinate values of X, Y, and Z are non-dimensional values from 0% to 100% convertible to dimensional distances by multiplying the Cartesian coordinate values of X, Y and Z by a height of the airfoil defined along a Z axis; the X and Y values of the pressure side are coordinate values that, when connected by smooth continuing arcs, define pressure side sections of the pressure side portion of the nominal airfoil profile at each Z coordinate value, the pressure side sections being joined smoothly with one another to form the pressure side portion; and the X and Y values of the suction side are coordinate values that, when connected by smooth continuing arcs, define suction side sections of the suction side portion of the nominal airfoil profile at each Z coordinate value, the suction side sections being joined smoothly with one another to form the suction side portion.
 14. The turbine engine of claim 13, wherein the turbine engine comprises a gas turbine having a compressor, a combustor, and a turbine; and wherein the airfoil is included within a nozzle in the turbine.
 15. The turbine engine of claim 14, wherein the nozzle is a second stage nozzle in the turbine.
 16. The turbine engine of claim 14, wherein the nominal airfoil profile lies in an envelope within +/−20% of a thickness of a trailing edge of the airfoil in a direction normal to any of the suction side and pressure side sections; and wherein: a height of the suction side portion is defined along the Z axis, and wherein the height of the suction side portion is less than or equal to the height of the airfoil; and a height of the pressure side portion is defined along the Z axis, and wherein the height of the pressure side portion is less than or equal to the height of the airfoil.
 17. The turbine engine of claim 16, wherein the height of the suction side portion and the height of the pressure side portion are substantially the same; wherein the height of the suction side portion and the height of the pressure side portion are each equal to or greater than 50% of the height of the airfoil; and wherein the suction side portion and the pressure side portion start at a common distance relative to a base of the airfoil and extend toward a tip of the airfoil.
 18. The turbine engine of claim 17, wherein the height of the suction side portion and the height of the pressure side portion are each equal to or greater than 75% of the height of the airfoil.
 19. The turbine engine of claim 17, wherein the height of the suction side portion and the height of the pressure side portion are each equal to or greater than 100% of the height of the airfoil.
 20. The turbine engine of claim 17, wherein the turbine comprises a second stage that includes a row of second stage nozzles adjacent to a row of second stage rotor blades; and wherein a plurality of second stage nozzles contained within the row of second stage nozzles comprises the airfoil. 